Circular no. 8i6 <fi 

August 1949 Washington, D.C. 




UNITED STATES DEPARTMENT OF AGRICULTURE 


Grasshopper Egg-Pod Distribution in the 
Northern Great Plains and Its Relation 
to Egg-Survey Methods 


By E. G. E)avis, entomologist, Division of Cereal and Forage Insect Investigations , and 
F. M. \y adley, statistical consultant, Bureau of Entomology and Plant Quarantine, 
Agricultural Research Administration 1 


CONTENTS 

o / 

Page 


Introduction.. . 2 

Sources of data. 2 

Egg-pod distribution. 3 

In relation to types of 

vegetation habitats. 3 

In fields and margins.* 4 

Sampling and survey methods. 8 

Number and location of 

field-sample units. 9 


SB 945 
.L7 D23 
Copy 1 


Page 

Sampling and survey methods, Cont’d 


Distribution of units within fields 9 
Number of field stops for a 

county or district. 10 

Distribution of stops within a 

county or district. 11 

Time utilization of sampling.... 12 

Discussion. 14 

Conclusions. 15 


iThe authors acknowledge the assistance given by J. R. Parker, in charge of the 
Bozeman, Mont., laboratory, Division of Cereal and Forage Insect Investigations, in 
both the field work and the preparation of the manuscript and by C. M Packard, in 
charge of the Division, for helpful criticism. Members of the staffs of the Montana 
State entomologist’s office, the Division of Grasshopper Control, and the Bozeman 
laboratory aided in much of the field work. 


lAot* 


.ogrop* 


















2 


CIRCULAR 816, U. S. DEPARTMENT OF AGRICULTURE 


INTRODUCTION 

G rasshopper surveys supply the preliminary information needed for 
the most economical and successful conduct of control campaigns. 
This basic information consists of (1) the location and extent of the in¬ 
festation, and (2) its density. An important consideration pertaining to 
grasshopper surveys is their timeliness. The most successful control cam¬ 
paigns are necessarily planned well in advance of the field work, and 
surveys made early enough must maintain their reliability up to the 
time field control work begins. An egg survey made in the fall of the year 
gives the best results. 

For at least 25 years grasshopper surveys have been employed to pre¬ 
dict future populations. During that time the survey has evolved from 
one of reconnaissance to the present standardized type in which infesta¬ 
tions are classified into categories based on the number of egg pods per 
square foot of soil sampled. 23 Fall egg surveys are conducted by the 
Division of Grasshopper Control throughout the area subject to severe 
grasshopper damage, which includes nearly all the States west of the 
Mississippi River. Usually, .however, it is necessary to survey only a 
portion of this area in any one year. It has been customary to sample an 
average of 7 to 11 fields representative of each county, to obtain mean 
egg-pod populations. 

The egg survey is yielding serviceable results. In its present form, 
however, it requires a fairly large personnel and a great deal of travel. 
Delays due to adverse weather during the period available for surveying 
add to the labor problem. Any improvement that could reduce, without 
loss of accuracy, either the labor or the travel involved would result in a 
considerable saving of money. It also seems probable that some gain in 
accuracy can be obtained. Although it is evident that nothing can be 
done about the size of the area to be surveyed or about the prevailing 
weather, it is believed that field and county sampling methods can be 
improved. 

The conclusions drawn from the data presented in this paper have 
been found to apply to conditions prevailing in the northern Great Plains, 
where the species Melanoplus mexicanus (Sauss.) was dominant while the 
data were being obtained. Whether they will apply to other areas or 
species has not been determined; however, many of the principles of 
sampling will be applicable. The present paper is on the application of 
these and other related studies to problems of field population and sam¬ 
pling, especially to immediate problems of survey. 

SOURCES OF DATA 

Intensive studies of grasshoppers in typical environments were initiated 
by the Bureau's grasshopper research station at Bozeman, Mont., in 
1931. The studies were conducted on eight areas, each approximately 2 


2 Shotwell, R. L. a method for making a grasshopper survey. Jour. Econ. 
Ent. 28: 486-491. 1935. 

3 -SOME PROBLEMS OF THE ANNUAL GRASSHOPPER SURVEY. Jour. Econ. Ent. 311 

523-533. 1938. 




^ 13 ?£Z 


3 


V GRASSHOPPER EGG-POD DISTRIBUTION 

.miles wide and 4 miles long, in Montana, North Dakota, and South 
Dakota. One of the main objectives was to test and improve grasshopper- 
survey methods. 

In the egg surveys made during the earlier years of the studies, 10 or 
more 1-square-foot samples were taken on every quarter section of land. 
By 1938 doubt had arisen as to whether the number of samples taken on 
the areas was too few or too many, and whether taking a fixed number 
of samples per unit area is the most accurate way of determining mean 
egg-pod populations in the various crops and habitats. That the personnel 
charged with conducting the general surveys were also in doubt regarding 
the adequacy of sampling is evident from the changes made in the sam¬ 
pling instructions given the surveyors. To determine the dependability 
of sampling procedure several counties were surveyed in sufficient detail 
to obtain data for statistical analysis. 

The first special intensive egg survey was conducted in the fall of 1939 
in Fergus and Judith Basin Counties, in north-central Montana. With 
the aid of one member of the general survey staff, 200 fields were exam¬ 
ined in 2 counties, which were treated as a single unit. In 1940, with the 
assistance of survey personnel supplied by the Division of Grasshopper 
Control and the Montana State entomologist, special egg surveys were 
conducted in 10 counties in north-central Montana, 70 fields in each 
county being sampled. The last of the special egg surveys was conducted 
in Davison and Brown Counties, South Dakota, in 1942. After the special 
county egg surveys were completed, the data from them and from the 
study areas were analyzed by methods developed along the lines shown 
by Snedecor. 4 

EGG-POD DISTRIBUTION 

In Relation to Types of Vegetation Habitats 

In any adequate study of sampling methods the distribution of the egg 
pods among the different habitats must be considered. Although it has 
been common knowledge for years that grasshoppers are selective in their 
egg-laying habits, accurate comparisons of the egg populations in habi¬ 
tats were lacking. Intensive studies were made, therefore, of egg-pod 
distribution in fields and field margins. 

Records of egg populations in different plant associations on the 
northern Great Plains study areas for the 8-year period 1936-43 are 
summarized in table 1. It can readily be seen that some habitats, such 
as field margins and idle land, contain greater egg concentrations than 
others. As to egg-pod category, the first four habitats listed could be 
classed as high, the next four as medium, and the last five as low. Plowed 
and fallowed lands, not listed in the table, had practically no egg pods. 
Although the position of each habitat varied somewhat from year to 
year, as compared with its 8-year average, most of the variations were 
not great enough to change a habitat from one category to another. This 
tendency to remain in about the same relative position from year to year 
led to the idea that a single habitat might be used in carrying on the 
general survey. 


4 Snedecor, G. W. statistical methods, Ed. 3, 422 pp., Ames, Iowa. 1940. 



4 


CIRCULAR 816, U. S. DEPARTMENT OF AGRICULTURE 


Table 1 .—Average egg-pod distribution per square foot by habitats for areas 
under study in the northern Great Plains, 1936-43 


Habitat 

1936 

1937 

1938 

1939 

1940 

1941 

1942 

1943 

Average 

1936-43 

Field margins.. . 

0.761 

0.741 

1.241 

0.725 

0.862 

0.773 

0.976 

0.816 

0.862 

Idle land. 

.581 

.394 

.654 

.624 

.519 

.615 

.553 

.440 

.547 

Pasture. 

.400 

.240 

.575 

1.000 

.301 

.300 

.095 

.385 

.412 

Legumes. 

.278 

.514 

.421 

.574 

.418 

.353 

.355 

.314 

.403 

Flax stubble. 





.101 

.718 

.267 

.317 

.351 

Small-grain 










stubble. 

.336 

.546 

.356 

.587 

.249 

.259 

.279 

.162 

.347 

Prairie. 

.526 

.387 

.369 

.305 

.389 

.293 

.120 

.169 

.320 

Crested 










wheatgrass. . . 

.375 

.600 

.580 

.280 

.140 

.175 

.182 

.196 

.316 

Wild-hay 










meadows. 

.000 

.250 

.730 

.090 

.214 

.280 

.040 

.000 

.200 

River-bottom 










land. 

.050 

.000 

.330 

.000 

.330 

.120 

.200 

.120 

.144 

Truck crops.... 

.390 

.207 

.133 

.210 

.006 

.107 

.000 

.013 

.133 

Corn. 

.165 

.174 

.180 

.104 

.134 

.190 

.032 

.023 

.125 

Sorghums. 




.185 

.249 


.027 

.000 

.115 












The data in table 1 are quantitative only to the extent that they indi¬ 
cate the egg-pod density in the respective habitats. To apply these data 
to general field conditions, the percentage of the total area occupied by 
each habitat must be considered. For example, although of all the habi¬ 
tats field margins contain the heaviest populations, they comprise only 
about 5 percent of the total area. Conversely, small-grain fields, which 
have moderate populations, comprise about 80 percent of the farmed area. 
In the 10-county special survey, grainfields predominated and crop dif¬ 
ferences were not prominent; hence, crop-type differences were not con¬ 
sidered in further analysis of these data, except for distinction between 
field and margin. 

In Fields and Margins 

One of the first essentials in the development of a dependable survey 
method is a knowledge of egg-pod distribution within fields. One opinion 
was that more eggs were laid near the edge of the field than near the 
center. To obtain more definite data, egg sampling was conducted in 10 
counties in north-central Montana, samples being taken from 70 fields 
located at random in each county. The number of fields of each major 
crop sampled was in proportion to the acreage of that crop in the county. 
In each field 5 pairs of -square foot units of soil were taken at equal 
distances apart in a straight line from the edge of the field to the center. 
Ten F 2 _s quare-foot units were also taken in the uncultivated margin 
of each field, 5 units in the half nearest the crop, and the other 5 in the 
half nearest the road. 

The mean egg-pod population for each field and margin location is 
shown by counties in table 2. It will be noted that populations for the 
different locations within fields tended to vary at random. In the margins 
numbers tended to be greater in the half near the field than in the half 
near the road. 

























GRASSHOPPER EGG-POD DISTRIBUTION 


5 


Table 2. Mean egg-pod populations per square foot in fields and margins 
in 10 counties in north-central Montana in 1940. (Five field and 2 mar¬ 
ginal locations were sampled at each of 70 different places in each county) 


County 

Field locations 1 

Marginal locations 

1 

2 

3 

4 

5 

Near road 

Near field 

Blaine. 

0.80 

0.33 

0.56 

0.63 

0.63 

0.75 

0.89 

Cascade. 

.48 

.44 

.64 

.86 

.30 

.56 

.72 

Chouteau. 

.64 

.64 

.36 

.33 

.34 

.79 

1.00 

Fergus. 

.62 

.30 

.32 

.38 

.46 

.48 

.84 

Hill. 

.20 

.26 

.42 

.50 

.64 

.82 

1.56 

Judith Basin. 

.14 

.04 

.10 

.19 

.04 

.06 

.10 

Liberty. 

.34 

.23 

.46 

.43 

.36 

.55 

.80 

Pondera. 

.56 

.79 

.66 

.96 

.89 

2.50 

2.91 

Teton. 

.59 

.67 

.49 

.49 

.63 

1.85 

1.90 

Toole. 

.34 

.34 

.53 

.39 

.44 

.43 

.58 

Average. 

.47 

.40 

.45 

.52 

.47 

.88 

1.13 


Locations designated by numbers: (1) Edge of field; (2) one-fourth of the distance to center of field; 
(3) one-half of the distance to center of field; (4) three-fourths of the distance to center of field; (5) center 
of field. 


To obtain further information on the effect of sample location, the 
data were studied by an analysis of variance. The results are shown in 
table 3. The arrangement of the sampling makes it possible to study the 


Table 3. —Variance in numbers of egg pods per square foot between fields, 
between locations within fields, and between units within locations, for 10 
counties in north-central Montana in 1940 (degrees of freedom given in 
parentheses in column heading) 


County 

Between 

fields 

(69) 

Between 

locations 

(4) 

Interaction, 
field and 
location (276) 

Units within 1 
locations 
(350) 

Blaine. 

n.oi 

3 1.02 

0.33 

0.42 

Cascade. 

2 .93 

3 1.60 

3 .50 

. 35 

Chouteau. 

2 .80 

3 .93 

.31 

.36 

Fergus. 

3 .50 

.63 

.30 

.32 

Hill. 

2 1.07 

1.03 

.45 

.42 

Judith Basin. 

3 .09 

3 .14 

.05 

.07 

Liberty. 

2 .37 

.28 

.24 

.16 

Pondera. 

2 .60 

.92 

.42 

.38 

Teton. 

2 1.44 

.25 

2 .82 

.47 

Toole. 

2 .68 

.22 

.18 

,24 


‘Interaction, field and location, is typically error for location; units is error for interaction and for fields 
in comparing variances by the F test. 

Significant at 1-percent level of probability. 

Significant at 5-percent level of probability. 


over-all effect of given locations in the field, as well as the interaction or 
differential effect of location from field to field. The variation between 
units, as shown within pairs at each location, can also be studied. As 















































6 


CIRCULAR 816, U. S. DEPARTMENT OF AGRICULTURE 


might be expected, there was a significant difference between field popu¬ 
lations. In all but 2 counties (Fergus and Judith Basin) the differences 
were highly significant. The differences between populations in the 5 
different within-field locations, however, showed a slight tendency toward 
significance in only 4 of the 10 counties, as seems apparent from a com¬ 
parison of the averages in table 2. 

It should make no material difference, therefore, where the units are 
taken within fields if they are fairly well distributed. Some data of this 
type might be considered to need transformation before analysis, but 
population levels were rather uniform, and the total number of egg pods 
found in each designation was high enough so that little or no gain could 
be expected from the transformation. 

The results of an analysis of the data for the field margins are given 
in table 4. These results are similar to those for the fields. Population 

Table 4. —Variance in numbers of egg pods per square foot between field 
margins, between locations within margins, and between units within the 
locations, for 10 counties in north-central Montana in 1940; }/%-square- 
foot sample units (degrees of freedom given in parentheses in column 
headings) 


County 

Between 

field 

margins 1 

(69) 

Between 
locations 
within 
margins (1) 

Interaction, 
field and 
location 
(69) 

Between units 
within 
locations 
(560) 

Blaine. 

1.12 

0.82 

20.54 

0.39 

Cascade. 

.81 

1.04 

.42 

.38 

Chouteau. 

4.23 

1.90 

.87 

1.02 

Fergus. 

2.99 

2 5.32 

1.22 

1.33 

Hill. 

8.62 

2 29.61 

L5.07 

3.29 

Judith Basin. 

.13 

.07 

.04 

.05 

Liberty. 

1.19 

22.76 

.56 

.48 

Pondera. 

6.16 

7.20 

3.98 

4.13 

Teton. 

11.33 

.08 

5.20 

6.49 

Toole. 

.86 

.97 

.46 

.37 



‘Significant at 1-percent level of probability. 
“Significant at 5-percent level of probability. 


variations between field margins were highly significant for all 10 coun¬ 
ties. Populations in the two halves of the margins were not significantly 
different in 7 of the 10 counties. 

In general, the analyses show highly significant variations in the 
numbers of egg pods present in different fields and field margins. On the 
other hand, the variations between locations within fields or field margins 
had very little, if any, significance. 

In order to make a more detailed comparison of the numbers of egg 
pods per square foot, 10 wheat-stubble fields in a single South Dakota 
locality were extensively sampled in 1942. Fifty pairs of }/% -square-foot 
units from the same locations were taken in each. The pairs were taken 
from similar uniformly distributed locations in each field. The popula¬ 
tions in the different fields ranged from 0.14 to 0.93 egg pod per square 
foot. Analysis of variance of the pairs is shown in table 5. 




















GRASSHOPPER EGG-POD DISTRIBUTION 


7 


Table 5. —Variance in numbers of egg pods per % square foot in one 
locality in South Dakota 


Areas sampled 

Degrees of freedom 

Mean square 

Between fields. 

9 

U.16 

Between locations within the same fieid. 

490 

2 .26 

Between units within the same location . . 

500 

.20 


‘Significant at 1-percent level of probability. 
Significant at 5-percent level of probability. 


As was expected, the field-population differences were highly signifi¬ 
cant. Population variations due to locations within fields were significant, 
but the difference was not great and probably could not have been 
recognized, except for the large number of samples involved. 

It has been pointed out that in some habitats, such as small-grain 
stubble, the number of egg pods approximated fairly consistently the 
average number in all the habitats (table 1). This fact, plus the fact that 
small grain is well distributed over the northern Great Plains, suggested 
the possibility that this habitat alone might be used in conducting the 
general survey. The experimental sampling both in grainfields and in 
other common types of habitat in two central Montana counties in 1939 
seemed to indicate the reliability of such procedure. 

Further evidence on this phase of the problem was obtained from the 
10-county survey in north-central Montana in 1940. The average egg-pod 
populations for all fields, all margins, grainfields, and fields other than 
grain and their margins are given in table 6. Since field margins comprise 


Table 6 . —Mean egg pod populations per square foot for fields, margins, 
weighted fields and margins, grain-stubble fields, and fields other than 
grain and their margins in 10 counties in north-central Montana in 19^0 


County 

All 

fields 

All 

margins 

All 

fields 

and 

margins 

Grain- 

stubble 

fields 

Fields 
other than 
grain and 
their 
margins 

Blaine . 

0.59 =*= 0.07 

0.83 =*=0.08 

0.60 =*= 0.06 

0.40=*=0 

.03 

0.82 =*=0.12 

Cascade. 

.52=*= 

.07 

.65=*= 

.08 

.53=*= .06 

.41=*= 

.07 

.68=*= .11 

Chouteau. 

.46=*= 

.06 

.90=*= 

.16 

.48=*= .06 

.36=*= 

.05 

.87=*= .17 

Fergus. 

,41=t 

.06 

. 66=*= 

.14 

.42=*= .05 

.37=*= . 

.08 

.47=*= .07 

Fergus 1 . 

1.80=*= 

.16 

2.87=*= 

.77 

1.85=*= .15 

1.91=*= . 

,18 

1.40=*= .27 

Hill . 

.40=*= 

.08 

1.21=*= 

.22 

.44=*= .07 

.44=*= . 

.08 

.46=*= .18 

Judith Basin . 

. 10=*= 

.02 

.08=*= 

.03 

.10=*= .02 

.11=*= . 

.03 

.08=*= .03 

Liberty. 

.36=*= 

.05 

.68=*= 

.08 

.38=*= .04 

.36=*= . 

.05 

.53=*= .14 

Pondera. 

.77=*= 

.06 

2.70=*= 

.19 

.86=*= .05 

.77=*= . 

,06 

1.01=*= .09 

Teton. 

.58=*= 

.10 

1.87=*= 

.26 

.64=*= .09 

.48=*= . 

09 

1.20=*= .24 

Toole. 

.41=*= 

.05 

.51=*= 

.07 

.41=*= .05 

.41=*= . 

06 

,41± .07 


‘1939 survey. 


only about 5 percent of the total farm area, the averages for fields and 
for margins were given weights of 95 and 5, respectively, in obtaining 



























8 CIRCULAR 816, U. S. DEPARTMENT OF AGRICULTURE 

the means given in the columns “All fields and margins and Fields 
other than grain and their margins.” It may be seen that the popula¬ 
tions in field margins ran consistently higher than did those in the fields; 
however, the weighted means for both fields and margins were only 
slightly greater than those for the fields. A comparison of the weighted 
means for fields and margins with the means for the grain-stubble fields 
alone shows that the two groups of figures are close together. Possibly 
the most critical comparison is that of the average populations in small- 
grain stubble with those in the fields other than small grain and their 
margins, given in the last two columns. These sets of figures, although 
somewhat farther apart, still are close enough together to allow the grain- 
field figures to serve as a fairly reliable estimate of the general population. 
As a rule, grainfield populations appear the lighter. Standard errors of 
weighted averages are calculated as shown by Snedecor. 5 

Although these data substantiate the theory that the populations in 
grain stubble are a reliable index of the general population, there are 
reasons why it would not be advisable to sample grain stubble only. In 
the first place, small-grain fields, which comprise about 80 percent of the 
farmed acreage in the northern Great Plains, represent a preponderance 
of the agricultural area; therefore a general survey of this region, with 
stops prorated among the different habitats, would automatically be made 
up largely of small-grain fields. In the second place, the inclusion of the 
20 percent of nongrain fields and field margins would provide for explora¬ 
tory sampling to locate concentrations that otherwise might not be 
discovered. 


SAMPLING AND SURVEY METHODS 

In studying survey methods, the general nature of the population 
studied must be considered. If egg-pod distribution were entirely random, 
it would conform to the Poisson series, 6 and samples would reflect this 
distribution. In practice, a departure from the random or Poisson condi¬ 
tion occurs, population being “bunched,” and this departure is greater 
in dense infestations. In many sparse infestations the Poisson is nearly 
realized. In dense infestations variation is absolutely greater and pro¬ 
portionally less than in light ones. 

The nearness to the Poisson, or random, distribution can be judged by 
the variance. In a true Poisson series the variance is equal to the mean. 
In the typical “bunched” condition the variance becomes greater than 
the mean. Under field conditions it is practically never found to be less 
than that of the Poisson. For this reason a greater degree of precision 
than that limited by the total number of sample units and a variance 
equal to the mean cannot be expected. An example may be drawn from 
the analysis of variance of the South Dakota data (table 5). In this 
rather sparse infestation the mean was 0.18, the variance between adja¬ 
cent units was 0.20, and that between units well separated in the field 
was 0.26. 


5 See p. 3, footnote 4, (ch. 17). 

6 The Poisson series is explained by Snedecor’s text (see p. 3, footnote 4). It is 
based on simple probability in population problems such as this, of the numbers of 
units with no egg pods, and with one, two, or more. 



GRASSHOPPER EGG-POD DISTRIBUTION 


9 


Number and Location of Field-Sample Units 

Data presented above show that populations vary considerably more 
between fields than between units within fields, that there is a tendency 
to greater variation between distant units in a field than between adja¬ 
cent units, but that in light populations neither type of variation is 
pronounced. Two adjacent units of square foot each can be viewed as 
one 1-square-foot unit, thus affording a basis for comparing numbers and 
sizes of units. If two adjacent units were exactly similar, one would be 
as good as two, but if they differ greatly no special gain would come from 
spreading the sampling. 

The South Dakota data (table 5) has been used in calculating expected 
standard error of different combinations, using established methods. 7 
These calcu lations are given in table 7. 


Table 7. —The reliability of a grasshopper egg-pod survey based on different 
combinations of fields, field-sample locations, and units per field location 1 


Fields 

sampled 

Sample locations 
per field 

Units per sample 
location 

Standard error of 
mean egg pod 
population per unit 1 

Number 

Number 

Number 


20 

5 

1 

0.052 

20 

5 

2 

.042 

10 

10 

1 

.057 

10 

5 

2 

.059 

10 

5 

1 

.074 

10 

1 

10 

.077 

5 

5 

2 

.084 

10 

1 

5 

.089 


^ach field unit contained square foot. To place the standard error on a 1-square-foot basis it must 
be doubled. 


It can be seen that there is an advantage, but a very limited one, in 
spreading sampling within fields. Taking }^-square-foot units instead 
of 1-square-foot units, but doubling the number, will give only a slightly 
lower standard error. Taking the same number of units, but reducing 
their size by one-half, will increase the standard error considerably. To 
take all units in one place is going too far in the direction of “bunching” 
and increases the standard error markedly. In light infestations, such as 
the example just given, five 1-square-foot units are practically as good 
as twice the number of units half that size; but in denser infestations 
there would probably be more advantage in spreading within-field sam¬ 
pling. The five 1-square-foot units seem to offer a workable and sound 
combination. An increase in number of fields is more potent in reducing 
standard error than are increases in within-field sampling. 

Distribution of Units Within Fields 

The data in tables 2 and 3 show that location within the field has little 
systematic effect on the accuracy of the results. This fact indicates that 
sampling within the field need not follow an exact pattern that gives 


7 See p. 3, footnote 4 (sec. 17.8). 












10 CIRCULAR 816, U. S. DEPARTMENT OF AGRICULTURE 


fixed representation to parts near the center and the edge. A less exact 
plan of taking the samples over a large part of the field for example, an 
arc cutting well into the field and returning to the margin at another 
point—will do as well. 

Sampling in the field margin may be carried out as the worker returns 
to the car. It would seem feasible to cut down marginal sampling. Table 6 
shows that marginal populations had but little effect on weighted aver¬ 
ages. While they are higher and more variable than field populations, the 
margins constitute only a small proportion of the total area in the northern 
Great Plains. Taking only two 1-square-foot units in the margin will not 
mean much sacrifice in accuracy. 

All units should, of course, be located by some method that will preclude 
personal choice by the sampler. Randomness within fields is not essential 
in ordinary sampling, since the field itself is the primary sampling unit. 

Number of Field Stops for a County or District 

It has been shown that between-held variation is more important than 
that within held. In previous studies research workers have suggested a 
standard error of 0.125 egg pod per square foot as satisfactory. This level 
of precision is usually easier to reach in a low population than in a high 
one. It will be recalled that in the lightly infested area in South Dakota 
it could be achieved by moderate within-held sampling of 10 helds 
(table 4.). 

Using the data from the 10-county survey of north-central Montana, 
the authors attempted to determine the number of held stops needed for 
each county and for the 10 counties grouped together as a district. The 
held margins were taken into account, being weighted on the basis of 95 
percent for the helds, 5 percent for the margins. The allowable standard 
error of the mean was set at 0.125 egg pod per square foot. This concept 
of allowable standard error as a constant arithmetic hgure is a useful one 
for the level of populations usually encountered. For sparse populations 
it would lead to using only a small number of units (table 8) and some 
minimum should be specihed. 


Table 8. —Number of field stops necessary to survey each of 10 counties in 
Montana, allowing a standard error of 0.125 egg pod per square foot 


County 

Approximate 

population 

mean 

Stops needed to obtain a 
standard error of 0.125 in— 

Fields 

only 

Fields and 
margins 

Judith Basin. 

0.1 

3 

3 

Liberty. 

.4 

10 

9 

Toole. 

.4 

12 

12 

Fergus. 

.4 

13 

12 

Hill.*. 

.4 

28 

27 

Chouteau. 

.5 

21 

20 

Cascade. 

.5 

26 

24 

Blaine. 

.6 

26 

25 

Teton. 

.6 

37 

35 

Pondera. 

.8 

16 

15 



















GRASSHOPPER EGG-POD DISTRIBUTION 


11 


It will be recalled that 70 fields per county were sampled and the fields 
sampled were prorated among the different habitats according to their 
acreages Five pairs of K-square-foot samples were taken in each field 
and 10 1^-square-foot samples along each margin. The survey data 
were treated by using variance between fields within each county. The 
results are shown in table 8. 

Where the mean egg populations for the county ranged from 0.5 to 
0.8 pod per square foot, from 15 to 35 field stops were required in order 
to obtain county means within the prescribed standard error in a survey 
by counties. The average number of fields needed was 20. For county 
means of about 0.4 egg pod per square foot, from 9 to 27 fields, or an 
average of 15, were needed. In South Dakota, where the mean population 
was about 0.2 egg pod per square foot, 10 fields were adequate. For 
Judith Basin County, Mont., with a mean population of 0.1, only 3 
fields would have been necessary. Thus, it can be seen that the number 
of field stops needed per county for a survey on a county basis is largely 
affected by the population level. In low populations more than the cal¬ 
culated minimum just mentioned will be required for a representative 
survey. 

Variation between county populations was not marked, but with the 
large number of fields used (70 per county) it appeared as highly signifi¬ 
cant. Analyzing with field means as units, the variance between counties 
was 2.14 and between fields within counties 0.29. It was found, however, 
that the number of fields necessary to represent the district with the re¬ 
quired degree of precision was but a little greater than the number needed 
for a county having the same population level. 

Moderate numbers of fields per county tended to give an unsatisfactory 
standard error- for the county, and a standard error lower than needed 
for the mean of a group of similar counties. Less than 30 fields would 
have been required to give a standard error of 0.125 in the 10-county 
district considered (table 8); whereas for county units they total 182, and 
more would be required for representativeness in one or two of the 
counties. It is thus indicated that considerable economy might be effected 
by surveys of homogeneous groups of counties, rather than of individual 
counties as units. 

Since the number of stops required for a given standard error increases 
with the density of population, a procedure with some elasticity in number 
of fields would seem desirable. A given minimum (say 8 or 10) sufficient to 
provide representativeness might be surveyed. If the standard deviation 
were calculated among the first 10, the number required for the desired 
standard error (s x ) of the mean could be tentatively determined by solving 
the well-known equation s x = s V n in which s equals standard deviation 
among field means and n equals the number of fields. 

Distribution of Stops Within a County or District 

The field stops are the real sample units and their distribution is of 
considerable importance. To obtain complete randomness of distribution 
is not practical. In a statistical sense randomness is used in order to give 
every unit in a population a chance to be represented in the sample. 
Applications of error formulas in a strict sense are based on this concept. 


12 CIRCULAR 816, U. S. DEPARTMENT OF AGRICULTURE 

A rather systematic distribution of stops is better suited to many of the 
objectives of survey work. Three factors that must be provided for are 
as follows: (1) Representation of important sections and crop types, (2) 
plan of travel, (3) freedom from personal choice in selecting stops. In 
travel careful planning to obtain economy and coverage is required. In 
general, location of fields may be easily predetermined as at a given 
distance from some known point. 

A systematic sampling procedure, such as suggested, will tend to give 
more accurate results than random sampling. At the same time, if error 
is calculated as if the sample were fully random, the error estimate will 
tend to be too high. When the systematic sample gives results closely 
equivalent to results from a random sample, as often occurs in this work, 
there will not be much inaccuracy in treating it as a random sample, and 
what inaccuracy there is will be on the conservative side. Some random¬ 
ness may be arranged after the three essential factors have been provided 
for. 

A restricted random-sampling plan, or stratified sampling, is often 
followed, in order to ensure that some units fall in each subarea of crop 
type. In such a plan the variance between types or subareas should be 
removed in calculating the sampling error, because the precision of such 
a survey is properly determined from the variance within the types or 
subareas, rather than between them. In this kind of sampling it may be 
difficult to arrange satisfactory stratification when the number of units is 
small. It may not be important, however, if areas are rather homogeneous, 
if one crop type is of outstanding importance, and if eggs are widely dis¬ 
tributed. In some other grasshopper-survey problems it may be important. 

If a large number of fields (25 or more) can be sampled, it may be 
possible to represent each important subdivision by several fields, pre¬ 
serving essential randomness in the location of these fields within the 
subdivisions. Randomness in location is easily achieved by some system 
of drawing numbers. Use of a group of similar counties as a unit may aid 
in attaining this objective and may ensure greater precision. If the number 
of fields is limited, it seems best to distribute them rather widely, select 
them by some objective method, and analyze the data as if the fields had 
been taken at random. The procedure described is not entirely correct, 
but it does not lead to serious mistakes. 

Time Utilization of Sampling 

A final evaluation of sampling plans may rest on the total possible cost. 
A plan giving the desired precision may be too expensive. Although sam¬ 
pling within fields is less important in reducing error than that between 
fields, it is less costly, and may give the best result in limiting the total 
expense of doing considerable work in a field, once the field is reached. 

Biometric theory enables us to determine the best distribution of 
samples between and within fields if we have some preliminary estimates 
of limitations on total cost, cost of sampling fields and units within 
fields, and between-field and within-field variances. For purposes of 
analysis, these costs have been estimated in terms of time requirements. 
The total cost of planning, reaching a field, writing up results, and other 
necessary work has been estimated at 1 hour. The total allowable time 


CIRCULAR 816, U. S. DEPARTMENT OF AGRICULTURE 13 

per county has been estimated from survey practice at 12 hours. The time 
required per -square-foot sample has been estimated at 2 minutes; or 
4 minutes for taking a sample from the field and a corresponding sample 
from the margin. It is probably true that overhead costs per field would 
be reduced if the number of fields were increased; however, for this 
approximate approach we must assume fixed costs. 

This application of biometric theory represents a departure from the 
practice of estimating the work required for a desirable standard error, 
such as 0.125 pod per square foot. It substitutes for this practice the find¬ 
ing of a work arrangement that will give as low a standard error as pos¬ 
sible under given limitations. This standard error may not be as low as 
would be desired, but it will be the lowest possible under the stated 
conditions. 

The variance for fields (V f ) over and above that expected from within- 
field variation is estimated by subtracting the mean square within fields 
from the mean square between fields and dividing by the number of units 
per field. It seems best for this calculation to pool within-field variances 
(for locations, interaction, and within locations), since they do not differ 
much and since the variance thus estimated will be that to be expected 
in general sampling. This procedure is illustrated by using data from 
table 3 for Cascade County. All within-field variance (weighted average) 
is estimated as 0.42; between-field variance is 0.93; V f — (0.93—0.42)/10 = 
0.05. V w is simply within-field variance. By us e of calculus, the best com¬ 
bination may be derived as follows: k = V (V W 'CD)/(V/C) and n = 
T /(C D-^-kC) , 8 where k = number of half-square-foot units per field, 
n = number of fields, CD = overhead cost per field, C = cost per unit, and 
T = total cost. For Cascade County, if T = 720 minutes, CD = 60, C = 4, 
we may calculate k= V (0.42X60)/ (0.05X4), or about 11. Then n = 
720/(60-j-(ll X4)], or about 7. The best combination is thus indicated as 
7 fields and 11 units per field. The variance of the county mean for this 
combination is estimated as 0.05/7-|-0.42/77, or 0.0126. The standard er¬ 
ror is V 0.0126, or a little over 0.11; doubled to apply to a square foot basis it is 
0.23. A practical demonstration by varying k may be made. If k is taken 
as 7 instead of 11, n will be 8; the variance of the mean will be 0.05/8— 
0.42/56, or 0.0137. If k is 15, n will be 6, and variance will be 0.05/6— 
0.42/90, or 0.0130. In either case the variance is increased, although a 
wide latitude in number of fields sampled and number of samples per 
field gives little change with these low variances. 

Similar calculations including samples from the field margins give 
similar results. Their inclusion in this analysis evidently makes little 
difference unless the variance ratio departs sharply from that of field 
samples. Hence the influence of modifying marginal sampling is ex¬ 
pressed as a reduction of the time required per field unit. In previous 
studies, the 2-minute period allowed for each field unit was doubled be¬ 
cause an equal number of units was taken in the margin. The possibilities 
in taking fewer units in the margins and thereby reducing the time per 
within-field sample to 3 minutes per unit, as well as in allowing 16 hours 


»If it is desired to estimate k and n for constant standard error and minimum cost, 
k will be estimated as above and n as (K. V f + V w )/{K'V m ), where V m is the square 
of the standard error of the mean. 







14 


CIRCULAR 816, U. S. DEPARTMENT OF AGRICULTURE 


instead of 12, have been tested. Approximate best combinations for these 
conditions and estimated standard errors have been worked out and are 
presented in table 9. 


Table 9. —Estimated best combinations for field sampling to determine 
grasshopper egg-pod distribution, with limited total cost, in north-central 
M ontana 


County 

Variance 

Best combinations and resulting standard 
error per square foot 

Be¬ 

tween 

fields 

C v f ) 

Within 

helds 

(V w ) 

12-Hour total 

16-hour total, 

(3 minutes 
per unit) 

4 minutes 
per unit 

3 minutes 
per unit 

Blaine. 

0.06 

0.38 

17 X10 

2 0.24 

18 Xll 

2 0.22 

HO Xll 

2 0.20 

Cascade. 

.05 

.42 

7 Xll 

.23 

7 X 13 

.21 

10 X 13 

.18 

Chouteau. 

.05 

.34 

7 X 10 

.22 

8 X 12 

.20 

10 X 12 

.18 

Fergus. 

.02 

.31 

6X15 

.17 

6X18 

.16 

8X18 

.14 

Hill. 

.06 

.44 

7 X 10 

.24 

8 X 12 

22 

10 X 12 

.20 

Judith Basin.... 

.00 + 

.06 

5X17 

.07 

6 X 20 

!06 

8 X 20 

.05 

Liberty. 

.02 

.20 

7X12 

.15 

7X14 

.14 

9X14 

.12 

Pondera. 

.02 

.40 

5 X 17 

.19 

6 X 20 

.16 

8 X 20 

.14 

Teton. 

.08 

.62 

7 Xll 

.28 

8 X 12 

.26 

10 X 12 

.23 

Toole. 

.05 

.21 

8X8 

.20 

8X9 

.19 

11X9 

.16 


l n (number of fields) X k (number of J+square-foot units per field), 
standard error per square foot for the combinations. 


In the general survey in north-central Montana a frequent combination 
is 7 or 8 fields per county and 10 units (5 square feet) per field. This is 
seen (table 9) to be a fairly efficient combination when cost is considered. 
With low population and small differences among fields, as in Fergus 
and Judith Basin Counties, Mont., the taking of more unit samples per 
field from fewer fields would seem to be practicable and economical. With 
higher populations and great between-held variation, the sampling of a 
larger number of fields with fewer within-held units would be better. In 
any event, it is necessary to sample a fairly large number of helds to avoid 
risk of missing altogether some important local infestation. 

DISCUSSION 

The hndings from these studies of egg-pod populations may be briefly 
summarized as follows: Variation between helds is dehnitely higher than 
that within helds. Variation between units within helds does not follow 
a dehnite location pattern. Although this variation is such as to make 
advisable the taking of unit samples from several well-separated locations 
in a held, little is gained by taking more than hve samples. Randomness 
is not needed within helds, but there should be freedom from personal 
choice. The reduction of area per unit from 1 square foot to square 
foot causes marked loss in precision unless the number is nearly doubled. 
Margins are higher and more variable in population than helds, but need 
not receive much consideration because of their comparatively small area. 





























GRASSHOPPER EGG-POD DISTRIBUTION 15 

In many instances from 15 to 30 fields are needed to obtain a satisfac¬ 
tory standard error of the area mean. For this purpose not many more 
stops will be required for a survey of several similar counties than would 
be needed for a single county. Distribution of stops over an area should 
provide for representation of principal subareas or types, should consider 
economy in travel, and should exclude personal choice. Randomness is 
desirable but may be hard to attain. It may be attained in part by sam¬ 
pling more fields per county or district. 

Several suggestions for improvement in efficiency of sampling have been 
considered. The greatest contribution to accuracy would be made by 
increasing the number of fields sampled, but this procedure would be 
rather expensive. Restriction of within-field sampling to permit increase 
in the number of fields is not promising, because so much work would be 
needed to sample only a few more fields. Modification of within-field 
sampling is also unpromising; increase in amount and distribution of 
more than five 1-square-foot units does not give much gain in informa¬ 
tion, and more “bunching” results in considerable loss. Surveying grain- 
fields alone does not seem to offer enough advantage to compensate for 
the reduction in information. Reduction in work in the margins seems 
well justified. Stratification, and also modification of number of fields in 
accordance with intensity of infestation, have been previously discussed 
and seem to have promise. Prediction of regional needs and transportation 
must be attacked before local distribution. 

The idea of consolidating similar and contiguous counties into a 
single district seems very promising. If there could be some lessening of 
dependence on county lines, adequate estimates could probably be made 
from fewer fields, travel could be planned more efficiently, and more 
representative sampling of important crop types could be carried out. 
Estimates of bait and transportation for regional needs could readily be 
governed by such a survey, although the utilization of county machinery 
might still be required to ascertain local distribution. The development of 
district sampling would make it easier to stratify and modify the intensity 
of the survey. Under this plan the total number of fields would be larger 
than for any single county, and greater freedom should be possible in 
planning for their selection. 


CONCLUSIONS 


It is suggested that five 1-square-foot units be examined in each field 
and two similar units in its margin. For convenience, the field units may 
be located on an arc cutting well into the field, and the sampler may 
return along the margin. Units should be taken by a method that would 
ensure freedom from personal choice. Stops should be distributed with 
respect to crops and localities so that the samples will be as representative 
as possible within the limitations of time and accessibility. Randomness 
is desirable but not fully attainable. A restricted random plan is worthy 
of study. Probably not less than 10 field stops should be made in a county 
or a group of similar counties, and 15 to 30 stops would be better. 


16 


CIRCULAR 816, U. S. DEPARTMENT OF AGRICULTURE 


The data presented in this circular indicate that increased accuracy and 
some reduction in the cost of surveys could be realized by using, as the 
survey unit, a group of similar counties, instead of a single county; by 
varying the number of stops within a county or district, above a fixed 
minimum, according to population, as indicated by preliminary sampling; 
and by stratification of sampling to ensure representation of important 
environments. 


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